The measurement of the cross section for the production of a
Z
boson, decaying to dielectrons or dimuons, in association with at least one bottom quark jet is performed with proton-proton collision data at
√
s
=
13
 
 
TeV
. The data sample corresponds to an integrated luminosity of
137
 
 
fb
−
1
, collected by the CMS experiment at the LHC during 2016–2018. The integrated cross sections for
Z
+
≥
1
 
b
 
jet
and
Z
+
≥
2
 
b
 
jets
are reported for the electron, muon, and combined channels. The fiducial cross sections in the combined channel are
6.52
±
0.04
(
stat
)
±
0.40
(
syst
)
±
0.14
(
theo
)
 
 
pb
for
Z
+
≥
1
 
b
 
jet
and
0.65
±
0.03
(
stat
)
±
0.07
(
syst
)
±
0.02
(
theo
)
 
 
pb
for
Z
+
≥
2
 
b
 
jets
. The differential cross section distributions are measured as functions of various kinematic observables that are useful for precision tests of perturbative quantum chromodynamics predictions. The ratios of integrated and differential cross sections for
Z
+
≥
2
b
 
 
jets
and
Z
+
≥
1
 
b
 
jet
processes are also determined. The value of the integrated cross section ratio measured in the combined channel is
0.100
±
0.005
(
stat
)
±
0.007
(
syst
)
±
0.003
(
theo
)
. All measurements are compared with predictions from various event generators.